I am really surprised to see that Welsh Rarebit has crossed the pond! (Albeit several decades ago.)
It is, at it's most basic, just cheese on toast. But the addition of English mustard (and it really does need to be that strong version in this - American mustard or French mustard will not do), and brown ale - again, not pale ale or lager - does elevate it to a rather different animal than just "cheese on toast".
I have made two different versions this year - one was thicker, and designed to go on toast, the other was just this week, and a more liquid sauce to go with cauliflower. I will find the older recipe and post both. (They were both delicious.)